3.1: OneStep Equations
Learning Objectives
At the end of this lesson, students will be able to:
 Solve an equation using addition.
 Solve an equation using subtraction.
 Solve an equation using multiplication.
 Solve an equation using division.
Vocabulary
Terms introduced in this lesson:
 equal
 equation
 isolate
 linear equation
Teaching Strategies and Tips
Use the introductory problem to motivate equivalent equations, since it can be solved two ways:
 The cost plus the change received is equal to the amount paid,
x+22=100 .  The cost is equal to the difference between the amount paid and the change,
x=100−22
Examples 1 and 2 are essentially the same; constant terms must be added to both sides to isolate
Additional Example.
Solve
Solution. To isolate
The variable in Example 3 is not the usual
Solve
Hint: To isolate
In Examples 46, teachers may opt to solve the equations by adding the opposite in lieu of subtracting.
Example.
Solve
Hint: To isolate
Use Example 6 as an example of an equation with fractions. Remind students to find common denominators.
Point out in Example 8 that in general,
which will help students isolate
Note that the equation in Example 10 can be written in dollars or in cents:

5x=3.25 (x in dollars) 
5x=325 (x in cents)
Although Examples 13 and 15 can be solved by making a table and Example 14 by guessing and checking, teachers are encouraged to help students setup and solve an equation of the type presented in the lesson.
Error Troubleshooting
General Tip: After the constant term is canceled in a onestep equation, the variable must be carried down onto the next line. Remind students to write the
General Tip: Students forget to perform the same operation on both sides of an equation. Have students use a colored pencil to write what they are doing to both sides of the equation.
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